Inflation in the 18-country bloc using the euro rose by just 0.5 percent in the year in May, significantly below the ECB's target of 2 percent, creating further worries for central bank head Mario Draghi as he mulls extra policy action.
The inflation slowdown has been due to lower energy costs and increasing euro strength, EY said, warning that there are "real concerns that inflation could turn to deflation, as firms start to bid down prices and wages in order to compete for orders".
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One result of deflation is to push down demand, as people hold off purchases in the hope of more price declines. It can also cause increased unemployment and even lead to economic depression.
The euro zone is already battling with a high unemployment rate, close to 12 percent, which is likely to keep wages low. But deflationary pressures could have a knock on effect on consumer spending, just as confidence was starting to build.
"While weak or negative inflation may be a positive development for consumers in the near term, a sustained period of deflation would dampen spending in the medium term, as it would both encourage consumers to delay major purchases and would squeeze employers' ability to increase or even sustain current wage levels," Rogers said.
Italy is set to grow by just 0.3 percent in 2014, according to EY, while Greece's economy will contract 0.3 percent and Cyprus' is seen shrinking 4.3 percent over the year.
In contrast, Spain and Portugal - two of the worst-hit countries during the sovereign debt crisis - are set for sharp pickups, EY said. These economies are forecast to grow in line with the euro zone average, underlining the divergence in the region's recovery.
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Spain and Portugal have been praised for implementing the reforms needed to turnaround their economies, and are beginning to reap the rewards, while the likes of France and Italy were slower off the mark and their economic growth is lagging.
Exporters, however, might be in for another tough year as the euro remains stubbornly strong, EY warned. The euro is currently trading around $1.35 against the dollar, down from peaks of $1.39 earlier in the year.
Euro zone export volumes grew by just 1.4 percent in 2013, however EY said growing global demand meant this could accelerate to 3.5 percent in 2014, and 3.8 percent the following year.